Hartree-Fock Theory

In Hartree-Fock (HF) theory the energy of a system is given as a sum of five components:

E_HF = E_NN + E_T + E_v + E_coul + E_exch

The nuclear-nuclear repulsion E_NN describes the electrostatic repulsion between the nuclei and is independent of the electron coordinates. In time-independent HF theory, the kinetic energy of the nuclei is not, but the kinetic energy of the electrons E_T is considered. Together with the nuclear-electron attraction energy E_v it depends on the coordinates of one electron. The classical electron-electron Coulomb repulsion energy E_coul and the non-classical electron-electron exchange energy E_exch depend on the coordinates of two electrons. Calculation of these last two terms constitutes the main effort in HF calculations and is also responsible for the unfavorable formal scaling of computational effort as the fourth power of basis functions used for the description of the wavefunction. The particular assumption made in HF theory is that each electron feels the other electrons only as an average charge cloud, but not as individual electrons. 

 

 https://www.cup.uni-muenchen.de/ch/compchem/energy/hf1.html